Date: Apr 1, 2013 5:11 PM
Author: Jesse F. Hughes
Subject: Re: Mathematics and the Roots of Postmodern Thought

david petry <david_lawrence_petry@yahoo.com> writes:

> On Monday, April 1, 2013 11:50:38 AM UTC-7, Jesse F. Hughes wrote:
>

>> I'm eager to believe you, oh, golly I am. But it feels like you're
>> making it up.

>
> You don't really seem to have the background needed to participate
> constructively in this discussion. The following is an actual quote
> from a serious and well-respected mathematician; I'm not just making
> it up:
>
> "The actual infinite is not required for the mathematics of the
> physical world" (Soloman Fefermanm, in an article titled "Is Cantor
> Necessary?")


This quote is not really representative of how applied mathematicians
work, though.

Applied mathematicians actually use real numbers. They use the tools
of real analysis and hence appear to use the theory of real numbers.

Hey, you missed a whole bunch of my questions. Let me repeat them
here:

----------------------------------------------------------------------

>> Can you give an example of some piece of mathematics that an applied
>> mathematician would choose to avoid, because it's not "falsifiable"?

>
> Cantorian set theory.


Aside from the fact that applied problems don't tend to require
infinite sets, what is your evidence that applied mathematicians avoid
Cantorian set theory because is allegedly unfalsifiable?

[[NOTE: I'm not asking for Feferman's view that ZFC is not necessary
for applied math, ut that it is NOT USED because IT IS NOT FALSIFIABLE.]]

>> And can you tell me whether the axioms of, say, the theory of real
>> numbers are falsifiable?

>
> I don't know what you are referring to by "the axioms of the theory
> of real numbers".


There are a number of different axiomatizations of R. Let's take the
first one Google provides:

https://en.wikipedia.org/wiki/Real_number#Axiomatic_approach

Are these axioms falsifiable? How do I tell?

[[NOTE: Still wondering.]]

>> Of course, if the theory of real numbers is not falsifiable, it would
>> seem you have a problem, right? Don't applied mathematicians (and
>> scientists!) use that theory regularly?

>
> The real numbers can be developed in the context of falsifiability,
> which should be obvious since scientists use real numbers.


Can you show me a falsifiable set of axioms for R and some indication
that this is a set of axioms that applied mathematicians use (because
scientists wouldn't have it any other way)?

[[NOTE: Still wondering about this, too.]]

> The real numbers that scientists use are finite precision real
> numbers, which can be thought of as rational numbers together with
> an error estimate. The theory of infinite precision real numbers
> can be developed as the limiting case when the error goes to zero.


Oh? So real scientists do not believe in pi, but only in
approximations to pi? And also, real scientists do not use, oh,
sqrt(2)?

That is fascinating!

Can you show me any published account (besides your own) which
indicates that scientists do what you say? Is there any scientist
ever who has actually published an exhortation to always treat pi as a
fiction and only use approximations to pi, because pi itself is part
of the unfalsifiable pseudoscience?

[[NOTE: still wanting an answer to the above questions.]]

----------------------------------------------------------------------

Your allegation that I am to ignorant to participate would sure seem
to be more plausible if you had answers to these questions.

Look, David, if you don't want to discuss your own half-baked ideas
with me, that's fine. You can say so. But stop pretending that you
have any clear grasp of what you're saying, since you've done NOTHING
to indicate what falsifiability means in a mathematical setting, aside
from some tired analogy of computer-as-microscope.

Just try and answer these perfectly natural questions, please.

--
"Many argue that its programmers have turned out shoddy programs, but
[their] objective is to make profit, not superlative programs per
se. By the profit criterion, Microsoft has been one of the greatest
companies in the history of this country." -- ADTI defends Microsoft